Global number field search results

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Degree	Signature	Galois group	Class number	Class group
Regulator	Num. ramified primes	Ramified primes		Unramified primes
CM field	Discriminant		Root discriminant

Results (displaying matches 1-50 of 141)

Label	Polynomial	Discriminant	Galois group	Class group
20.2.372703037695339609375744.1	x^20 - 2x^18 + 3x^16 - 2x^14 + 10x^12 + 5x^8 - 6x^6 - x^4 + 4x^2 - 1	\( -\,2^{10}\cdot 11^{16}\cdot 89^{2} \)	20T846	Trivial (GRH)
20.6.1667682586167898216778752.1	x^20 - 4x^19 + 2x^18 + 10x^17 - 23x^16 + 32x^15 - 8x^14 - 23x^13 - 33x^12 + 89x^11 - 83x^10 + 41x^9 + 51x^8 - 2x^7 - 88x^6 + 34x^5 - 6x^4 - 16x^3 + 23x^2 + 5x - 1	\( -\,2^{10}\cdot 11^{16}\cdot 23^{2}\cdot 67 \)	20T846	Trivial (GRH)
20.2.2732857610451081915433984.1	x^20 + 4x^18 + 8x^16 + 23x^14 + 35x^12 + 2x^10 - 24x^8 - 10x^6 - 8x^4 - 7x^2 - 1	\( -\,2^{10}\cdot 11^{16}\cdot 241^{2} \)	20T846	Trivial (GRH)
20.6.2732857610451081915433984.1	x^20 - 4x^18 - 2x^16 + 31x^14 - 51x^12 + 28x^10 - 12x^8 + 4x^6 + 10x^4 - 5x^2 - 1	\( -\,2^{10}\cdot 11^{16}\cdot 241^{2} \)	20T846	Trivial (GRH)
20.6.2732857610451081915433984.2	x^20 + 6x^18 + 6x^16 - 38x^14 - 105x^12 - 101x^10 - 37x^8 + 10x^6 + 14x^4 + 2x^2 - 1	\( -\,2^{10}\cdot 11^{16}\cdot 241^{2} \)	20T846	Trivial (GRH)
20.6.2732857610451081915433984.3	x^20 + 3x^18 + 7x^16 + 9x^14 - 10x^12 - 9x^10 - 53x^8 - 30x^6 + 45x^4 + 15x^2 - 1	\( -\,2^{10}\cdot 11^{16}\cdot 241^{2} \)	20T846	Trivial (GRH)
20.2.3254575989691824951510016.1	x^20 + 9x^18 + 36x^16 + 86x^14 + 142x^12 + 176x^10 + 159x^8 + 93x^6 + 32x^4 + 4x^2 - 1	\( -\,2^{10}\cdot 11^{16}\cdot 263^{2} \)	20T846	Trivial (GRH)
20.2.4099733414648735703133184.1	x^20 - 2x^18 - x^17 - 3x^16 - 5x^15 - 3x^14 - 25x^13 - 33x^12 + 16x^11 + 45x^10 + 44x^9 + 27x^8 - 50x^7 - 89x^6 - 13x^5 + 39x^4 + 16x^3 - 3x^2 - 3x - 1	\( -\,2^{10}\cdot 11^{17}\cdot 89^{2} \)	20T846	Trivial (GRH)
20.8.4902190169190997617688501.1	x^20 - 5x^19 + 8x^18 - 6x^16 - 34x^15 + 74x^14 + 102x^13 - 547x^12 + 775x^11 - 266x^10 - 574x^9 + 829x^8 - 424x^7 + 2x^6 + 142x^5 - 101x^4 + 22x^3 + 6x^2 - 4x + 1	\( 11^{16}\cdot 197^{2}\cdot 2749 \)	20T846	Trivial (GRH)
20.2.9068009358374390210642944.1	x^20 - x^18 - 2x^16 - 3x^14 - 9x^12 - 11x^10 - 19x^8 - 15x^6 - 4x^4 - 3x^2 - 1	\( -\,2^{10}\cdot 11^{16}\cdot 439^{2} \)	20T846	Trivial (GRH)
20.6.10086602384511078995362816.1	x^20 - 8x^18 + 29x^16 - 57x^14 + 67x^12 - 42x^10 - 9x^8 + 47x^6 - 43x^4 + 15x^2 - 1	\( -\,2^{10}\cdot 11^{16}\cdot 463^{2} \)	20T846	Trivial (GRH)
20.6.12671809176594786122989568.1	x^20 - 2x^19 + 3x^18 - 4x^17 + 3x^16 + 6x^15 - 2x^14 - 6x^13 - 39x^12 - 50x^11 - 11x^10 + 12x^9 - 66x^8 - 124x^7 - 69x^6 + 104x^5 + 315x^4 + 258x^3 + 41x^2 - 18x + 1	\( -\,2^{20}\cdot 11^{16}\cdot 263 \)	20T846	Trivial (GRH)
20.4.16452808797865383899862016.1	x^20 - x^19 - 5x^18 + 8x^17 + 11x^16 - 31x^15 - 36x^14 + 61x^13 + 61x^12 - 147x^11 - 37x^10 + 228x^9 - 20x^8 - 136x^7 + 172x^6 + 24x^5 + 32x^3 - 224x^2 + 160x - 32	\( 2^{10}\cdot 11^{16}\cdot 23^{2}\cdot 661 \)	20T846	Trivial (GRH)
20.6.24868623129665465017517056.1	x^20 + 4x^18 - 2x^16 - 20x^14 - 18x^12 - 6x^10 + 43x^8 + 84x^6 + 10x^4 - 6x^2 - 1	\( -\,2^{10}\cdot 11^{16}\cdot 727^{2} \)	20T846	Trivial (GRH)
20.10.24868623129665465017517056.1	x^20 - 2x^18 - 6x^16 + 19x^14 - 30x^12 - 28x^10 + 105x^8 - x^6 - 37x^4 + 12x^2 - 1	\( -\,2^{10}\cdot 11^{16}\cdot 727^{2} \)	20T846	Trivial (GRH)
20.6.24868623129665465017517056.2	x^20 + 7x^18 + 8x^16 - 34x^14 - 108x^12 - 112x^10 - 13x^8 + 43x^6 + 14x^4 - 4x^2 - 1	\( -\,2^{10}\cdot 11^{16}\cdot 727^{2} \)	20T846	Trivial (GRH)
20.10.24868623129665465017517056.2	x^20 + x^18 - 16x^16 - 17x^14 + 74x^12 + 90x^10 - 94x^8 - 112x^6 + 26x^4 + 5x^2 - 1	\( -\,2^{10}\cdot 11^{16}\cdot 727^{2} \)	20T846	Trivial (GRH)
20.10.24868623129665465017517056.3	x^20 - 3x^18 - 8x^16 + 27x^14 + 9x^12 - 71x^10 + 35x^8 + 49x^6 - 58x^4 + 19x^2 - 1	\( -\,2^{10}\cdot 11^{16}\cdot 727^{2} \)	20T846	Trivial (GRH)
20.6.24868623129665465017517056.3	x^20 + x^18 - 9x^16 - 18x^14 + 3x^12 + 35x^10 + 30x^8 - 7x^6 - 24x^4 - 10x^2 - 1	\( -\,2^{10}\cdot 11^{16}\cdot 727^{2} \)	20T846	Trivial (GRH)
20.10.24868623129665465017517056.4	x^20 + x^18 - 31x^16 + 59x^14 + 3x^12 - 86x^10 + 63x^8 + 15x^6 - 35x^4 + 12x^2 - 1	\( -\,2^{10}\cdot 11^{16}\cdot 727^{2} \)	20T846	Trivial (GRH)
20.0.31913046866560147064793841.1	x^20 - x^19 + 3x^18 - 3x^17 + 8x^16 - 6x^15 + 17x^14 - 12x^13 + 36x^12 - 29x^11 + 88x^10 + 80x^9 + 162x^8 + 42x^7 + 90x^6 - 42x^5 + 15x^4 - 15x^3 + 52x^2 + 20x + 23	\( 11^{16}\cdot 307^{2}\cdot 7369 \)	20T846	Trivial
20.4.35435556833879978012826721.1	x^20 - 10x^19 + 53x^18 - 192x^17 + 521x^16 - 1108x^15 + 1885x^14 - 2577x^13 + 2797x^12 - 2313x^11 + 1287x^10 - 215x^9 - 428x^8 + 523x^7 - 306x^6 + 81x^5 + 15x^4 - 19x^3 + 4x^2 + x + 1	\( 11^{16}\cdot 23^{3}\cdot 241\cdot 263 \)	20T846	Trivial (GRH)
20.6.36520333599375392823215104.1	x^20 + 8x^18 + 26x^16 + 40x^14 + 19x^12 - 33x^10 - 57x^8 - 14x^6 + 24x^4 + 10x^2 - 1	\( -\,2^{10}\cdot 11^{16}\cdot 881^{2} \)	20T846	Trivial (GRH)
20.0.67326616708750675935009901.1	x^20 - 5x^19 + 9x^18 - 5x^17 - 7x^15 + 7x^14 + 10x^13 + 5x^12 - 45x^11 + 27x^10 + 20x^9 - 2x^8 - 19x^7 - 9x^6 + 7x^5 + 22x^4 - 13x^3 - 6x^2 + 3x + 1	\( 11^{16}\cdot 131^{2}\cdot 85381 \)	20T846	Trivial (GRH)
20.8.128911494814978430027257081.1	x^20 - 10x^19 + 53x^18 - 192x^17 + 521x^16 - 1108x^15 + 1885x^14 - 2577x^13 + 2786x^12 - 2247x^11 + 1078x^10 + 225x^9 - 1088x^8 + 1249x^7 - 878x^6 + 378x^5 - 51x^4 - 52x^3 + 37x^2 - 10x + 1	\( 11^{16}\cdot 43\cdot 307\cdot 461^{2} \)	20T846	Trivial (GRH)
20.8.136172063462016753296264689.1	x^20 - 4x^19 + 4x^18 + 5x^17 - 34x^16 + 48x^15 + 54x^14 - 85x^13 - 50x^12 - 99x^11 + 87x^10 + 287x^9 - 27x^8 - 167x^7 - 45x^6 + 4x^5 + 52x^4 + 13x^3 - 30x^2 + 10x - 1	\( 11^{16}\cdot 23^{2}\cdot 571\cdot 9811 \)	20T846	Trivial (GRH)
20.8.197883941107619837212856549.1	x^20 - 10x^19 + 34x^18 - 21x^17 - 132x^16 + 240x^15 + 182x^14 - 680x^13 - 51x^12 + 1060x^11 - 98x^10 - 1067x^9 - 3x^8 + 738x^7 + 201x^6 - 331x^5 - 192x^4 + 71x^3 + 58x^2 - 1	\( 11^{16}\cdot 23\cdot 263^{2}\cdot 2707 \)	20T846	Trivial (GRH)
20.2.238025804044684565812451483.1	x^20 - 10x^19 + 54x^18 - 201x^17 + 570x^16 - 1296x^15 + 2438x^14 - 3872x^13 + 5258x^12 - 6146x^11 + 6197x^10 - 5383x^9 + 4005x^8 - 2520x^7 + 1299x^6 - 508x^5 + 118x^4 + 8x^3 - 19x^2 + 7x - 1	\( -\,11^{16}\cdot 23\cdot 397^{2}\cdot 1429 \)	20T846	Trivial (GRH)
20.6.330675770864580911767512064.1	x^20 - 22x^16 + 22x^14 + 11x^12 + 99x^10 + 121x^8 - 484x^4 - 484x^2 - 121	\( -\,2^{10}\cdot 11^{18}\cdot 241^{2} \)	20T846	Trivial (GRH)
20.10.330675770864580911767512064.1	x^20 - x^19 - 3x^18 + 7x^17 - 6x^16 + 11x^15 - 31x^14 - 68x^13 + 269x^12 - 140x^11 - 496x^10 + 705x^9 + 157x^8 - 799x^7 + 490x^6 + 374x^5 - 387x^4 + 57x^3 + 127x^2 - 25x + 1	\( -\,2^{10}\cdot 11^{18}\cdot 241^{2} \)	20T846	Trivial (GRH)
20.6.330675770864580911767512064.2	x^20 - 9x^18 - 11x^17 + 26x^16 + 66x^15 + 8x^14 - 99x^13 - 105x^12 - 22x^11 + 109x^10 + 77x^9 - 200x^8 - 308x^7 + 172x^6 + 374x^5 - 63x^4 - 165x^3 + 6x^2 + 11x + 1	\( -\,2^{10}\cdot 11^{18}\cdot 241^{2} \)	20T846	Trivial (GRH)
20.0.364876273903737477578853376.1	x^20 + 3x^18 - 8x^17 + 18x^16 + 5x^15 + 72x^14 + 12x^13 + 121x^12 + 272x^11 + 375x^10 + 242x^9 - 431x^8 - 323x^7 + 754x^6 + 519x^5 - 155x^4 - 284x^3 + 90x^2 + 125x + 43	\( 2^{10}\cdot 11^{17}\cdot 89^{3} \)	20T846	Trivial (GRH)
20.4.364876273903737477578853376.1	x^20 - 5x^19 + 6x^18 + x^17 + 10x^16 - 22x^15 - 31x^14 - 7x^13 + 312x^12 - 518x^11 + 254x^10 + 33x^9 + 236x^8 - 711x^7 + 678x^6 - 199x^5 - 145x^4 + 162x^3 - 66x^2 + 13x - 1	\( 2^{10}\cdot 11^{17}\cdot 89^{3} \)	20T846	Trivial (GRH)
20.0.364876273903737477578853376.2	x^20 - x^17 + 5x^16 + 7x^14 + 18x^13 + 142x^12 - 151x^11 + 241x^10 - 369x^9 + 1234x^8 - 962x^7 + 1121x^6 - 984x^5 + 1713x^4 - 1207x^3 + 183x^2 + 296x + 89	\( 2^{10}\cdot 11^{17}\cdot 89^{3} \)	20T846	Trivial (GRH)
20.4.364876273903737477578853376.2	x^20 - 6x^18 - 2x^17 + 16x^16 + 47x^15 + 84x^14 + 51x^13 + 91x^12 + 370x^11 + 418x^10 - 184x^9 - 1408x^8 - 2141x^7 - 435x^6 + 2072x^5 + 1857x^4 + 164x^3 - 364x^2 - 189x - 23	\( 2^{10}\cdot 11^{17}\cdot 89^{3} \)	20T846	Trivial (GRH)
20.2.658618684118710741619590144.1	x^20 - 16x^17 + 19x^16 - 22x^15 + 98x^14 - 186x^13 + 217x^12 - 384x^11 + 631x^10 - 684x^9 + 911x^8 - 1220x^7 + 904x^6 - 680x^5 + 1032x^4 - 976x^3 + 279x^2 + 10x + 43	\( -\,2^{10}\cdot 11^{16}\cdot 241^{3} \)	20T846	Trivial (GRH)
20.10.658618684118710741619590144.1	x^20 - 9x^18 + 18x^16 + 26x^14 - 80x^12 + 22x^10 - 93x^8 - 105x^6 + 780x^4 - 210x^2 - 241	\( -\,2^{10}\cdot 11^{16}\cdot 241^{3} \)	20T846	Trivial (GRH)
20.2.658618684118710741619590144.2	x^20 - 5x^17 + 8x^16 - 11x^15 - x^14 - 32x^13 + 52x^12 - 43x^11 + 103x^10 + 20x^9 - 145x^8 - 307x^7 - 295x^6 + 35x^5 - 948x^4 - 1141x^3 - 1008x^2 - 815x + 43	\( -\,2^{10}\cdot 11^{16}\cdot 241^{3} \)	20T846	Trivial (GRH)
20.10.658618684118710741619590144.2	x^20 - 3x^19 - 7x^18 + 4x^17 + 59x^16 + 41x^15 - 155x^14 - 151x^13 + 146x^12 - 149x^11 - 667x^10 + 273x^9 + 1109x^8 + 143x^7 - 550x^6 - 211x^5 + 94x^4 + 83x^3 - 7x^2 - 9x - 1	\( -\,2^{10}\cdot 11^{16}\cdot 241^{3} \)	20T846	Trivial (GRH)
20.6.658618684118710741619590144.2	x^20 - 7x^19 + 21x^18 - 39x^17 + 75x^16 - 174x^15 + 310x^14 - 368x^13 + 322x^12 - 235x^11 + 161x^10 - 175x^9 + 244x^8 - 314x^7 + 326x^6 + 310x^5 - 1506x^4 + 1501x^3 + x^2 - 808x + 353	\( -\,2^{10}\cdot 11^{16}\cdot 241^{3} \)	20T846	Trivial (GRH)
20.10.658618684118710741619590144.3	x^20 - 2x^19 - 10x^18 + 30x^17 + 2x^16 - 119x^15 + 241x^14 - 159x^13 - 305x^12 + 1042x^11 - 1683x^10 + 1548x^9 - 250x^8 - 1523x^7 + 2507x^6 - 1857x^5 + 376x^4 + 492x^3 - 472x^2 + 75x + 67	\( -\,2^{10}\cdot 11^{16}\cdot 241^{3} \)	20T846	Trivial (GRH)
20.6.766017076090168481174155747.1	x^20 - x^19 - 7x^18 + 15x^17 + 35x^16 - 88x^15 - 48x^14 + 257x^13 - 62x^12 - 671x^11 + 968x^10 - 291x^9 - 439x^8 + 503x^7 - 300x^6 + 20x^5 + 39x^4 - 77x^3 + 66x^2 + 14x - 1	\( -\,11^{16}\cdot 307\cdot 7369^{2} \)	20T846	Trivial (GRH)
20.4.876644133320296086383648593.1	x^20 - 10x^19 + 51x^18 - 174x^17 + 440x^16 - 868x^15 + 1376x^14 - 1786x^13 + 1927x^12 - 1760x^11 + 1398x^10 - 1001x^9 + 655x^8 - 368x^7 + 141x^6 + x^5 - 44x^4 + 28x^3 - 5x^2 - 2x + 1	\( 11^{18}\cdot 23^{3}\cdot 12959 \)	20T846	Trivial (GRH)
20.4.1156835869682281092646772177.1	x^20 - 10x^19 + 51x^18 - 174x^17 + 434x^16 - 820x^15 + 1177x^14 - 1233x^13 + 802x^12 - 15x^11 - 697x^10 + 938x^9 - 685x^8 + 255x^7 + 42x^6 - 130x^5 + 104x^4 - 57x^3 + 24x^2 - 7x + 1	\( 11^{16}\cdot 67\cdot 419\cdot 947^{2} \)	20T846	Trivial (GRH)
20.6.1394497058347173336049477687.1	x^20 - 10x^19 + 57x^18 - 228x^17 + 696x^16 - 1692x^15 + 3339x^14 - 5391x^13 + 7088x^12 - 7441x^11 + 5936x^10 - 3099x^9 + 293x^8 + 1279x^7 - 1413x^6 + 805x^5 - 239x^4 + x^3 + 27x^2 - 9x + 1	\( -\,11^{16}\cdot 23^{2}\cdot 131^{2}\cdot 3343 \)	20T846	Trivial (GRH)
20.6.2798446193101907881404399616.1	x^20 - x^18 - 5x^16 - 5x^14 - 3x^12 + 20x^10 + 27x^8 + 13x^6 + 15x^4 + 6x^2 - 1	\( -\,2^{20}\cdot 11^{16}\cdot 241^{2} \)	20T846	Trivial (GRH)
20.6.3009103398689521267119563776.1	x^20 - 5x^19 + 26x^17 - 20x^16 - 44x^15 + 5x^14 + 228x^13 - 440x^12 + 537x^11 - 716x^10 + 907x^9 - 836x^8 + 601x^7 - 442x^6 + 385x^5 - 335x^4 + 223x^3 - 88x^2 + 13x + 1	\( -\,2^{10}\cdot 11^{18}\cdot 727^{2} \)	20T846	Trivial (GRH)
20.10.3009103398689521267119563776.1	x^20 - 5x^19 + 26x^17 - 9x^16 - 44x^15 + 5x^14 - 47x^13 + 66x^12 + 218x^11 - 210x^10 - 314x^9 + 121x^8 + 931x^7 + 416x^6 - 1155x^5 + 28x^4 + 828x^3 - 176x^2 - 306x - 43	\( -\,2^{10}\cdot 11^{18}\cdot 727^{2} \)	20T846	Trivial (GRH)
20.6.3009103398689521267119563776.2	x^20 - 5x^19 + 15x^18 - 36x^17 + 74x^16 - 109x^15 + 69x^14 + 96x^13 - 356x^12 + 556x^11 - 892x^10 + 786x^9 + 744x^8 - 2285x^7 + 894x^6 + 868x^5 - 520x^4 - 85x^3 + 92x^2 - 17x + 1	\( -\,2^{10}\cdot 11^{18}\cdot 727^{2} \)	20T846	Trivial (GRH)
20.10.3009103398689521267119563776.2	x^20 - 5x^19 + 15x^18 - 47x^17 + 96x^16 - 142x^15 + 234x^14 - 146x^13 - 158x^12 + 160x^11 - 804x^10 + 1391x^9 - 136x^8 + 1213x^7 - 2923x^6 + 219x^5 + 470x^4 + 1345x^3 - 755x^2 - 160x + 89	\( -\,2^{10}\cdot 11^{18}\cdot 727^{2} \)	20T846	Trivial (GRH)